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Ideal Gas Law
-------------

An ideal gas is defined as one in which all collisions between atoms or molecules are
perfectly eleastic and in which there are no intermolecular attractive forces. One can
visualize it as a collection of perfectly hard spheres which collide but which otherwise
do not interact with each other. In such a gas, all the internal energy is in the form
of kinetic energy and any change in internal energy is accompanied by a change in
temperature.

PV = nRT

n = number of moles
R = Universal gas constant =  8.3145 J/mole K

Non-Ideal Gas Law
-----------------

The ideal gas equation makes some simplifying assumptions which are obviously not quite
true.  Real molecules do have volume and do attract each other.  All gases depart from
ideal behavior under conditions of low temperature (when liquefaction begins) and high pressure
(molecules are more crowed so the volume of the molecule becomes important).  Refinements to
the ideal gas equation can be made to correct for these deviations.

van der Waals equation:

As there are attractive forces between molecules, the pressure is lower than the ideal value.
To account for this the pressure term is augmented by an attractive force term a/V2.
Likewise real molecules have a volume.  The volume of the molecules is represented by the
term b.  The term b is a function of a spherical diameter d known as the van der Waals diameter.
The van der Waals equation for n moles of gas is:

(P + n2a/V2)(V - nb) = nRT

where a and b are empirically determined constants.